Discrepancies between Temp coefficients of Vmpp and Pmax

This is something that has been puzzling me for some time, while attempting to relate the observed performance of my array with the manufacturer's specifications. It seems like it is common for many panels to have a significant difference in the temperature coefficient of Vmpp and Pmax. In my case, Pmax drops by 0.45% for every degree C, but Vmpp apparently only drops by 0.35%. Looking around at other specifications for other panels, this sort of difference seems common, if not quite universal.

But this set my wondering, how is this the case? Unless I'm misunderstanding something, it seems to me that there are only two possible explanations:

An entirely different measuring methodology is used for these two coefficients, so no reasoning about their relationship is possible. This has been suggested to me before as an explanation, but it beggars belief slightly. I get that output measurements aren't always conducted in the most informative or realistic of ways, but it would seem astonishing that the measurement of two such closely related variables would be done in a way that makes it impossible to use them together - particularly given that it seems to be a more or less consistent pattern across many manufacturers.

Impp must also typically have a meaningfully negative temperature coefficient. This seems like the more likely explanation, but it contradicts what I thought I knew about the relationship between current and temperature. The temperature coefficient of Isc (which is often the only current coefficient quoted) is positive rather than negative; and from graphs that I have looked at, the shape of the curve generally doesn't change with temperature - it just gets shifted to the left on the voltage axis as the temperature rises.

Is there some subtlety I'm missing here? I know it's not a huge deal, but on a hot day that could easily by an additional 4% loss, and at the moment I simply don't understand where it comes from!

Comments

VMP is a measure of voltage which is just part of the equation measuring power. Pmax would the Power or Wattage. Since the current changes little there is less difference, since V x Amps(Current)= Wattage (or power)

Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites, Midnite E-panel, Prosine 1800 and Exeltech 1100, 660 ah 24v ForkLift battery. Off grid for @16 of last 17 years. Assorted other systems, and to many panels in the closet to not do more...lol

VMP is a measure of voltage which is just part of the equation measuring power. Pmax would the Power or Wattage. Since the current changes little there is less difference, since V x Amps(Current)= Wattage (or power)

Sure. But that's exactly my point. The coefficient of Vmpp is 0.1%/C smaller than the coefficient of Pmpp/Pmax. Given that (from what I understand) Impp remains relatively stable or even increases with temperature, I don't understand that.

Actually, I wasn't thinking about it as I typed, I guess they should drop at similar rates...

Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites, Midnite E-panel, Prosine 1800 and Exeltech 1100, 660 ah 24v ForkLift battery. Off grid for @16 of last 17 years. Assorted other systems, and to many panels in the closet to not do more...lol

It is not clear how you could observe these changes.Is this based on ambient temp? How would you measure cell temp?It is likely that an array will not have uniform cell temps. The hotter they get the greater the cell temp... and Vmp mismatching possibly.With 3 strings... 1 string that responds more to high temps would pull dow power more than Vmp.Then there is a question of the MPPT tracking? If the tracking is catching up to the real Vmp when it is getting warmer Vmp will stay higher then. I saw this on an Astronergy data sheet.Pmp coef. = -.469%/CVmp coef. = -.463%/CHave you checked this with a single module?

It is not clear how you could observe these changes.Is this based on ambient temp? How would you measure cell temp?It is likely that an array will not have uniform cell temps. The hotter they get the greater the cell temp... and Vmp mismatching possibly.With 3 strings... 1 string that responds more to high temps would pull dow power more than Vmp.Then there is a question of the MPPT tracking? If the tracking is catching up to the real Vmp when it is getting warmer Vmp will stay higher then. I saw this on an Astronergy data sheet.Pmp coef. = -.469%/CVmp coef. = -.463%/CHave you checked this with a single module?

You misunderstand, I think. This is not based on observation, this is coming from the spec sheet. The coefficients you quote are very close - but for my panels, and for many others I've seen, including e.g. samsung, these values are much further apart - around a tenth of a percent per C. The thing is, I don't understand how that can be the case unless the temperature coefficient of Impp is also meaningfully negative, which I don't believe it should be. How can power decrease faster than voltage with temperature, unless current is also decreasing with temperature?

It does have an example of where the Pmp is more temperature sensitive than Vmp would suggest (Imp temperature sensitively is the "opposite" of Vmp--Imp goes up (slightly) with increasing temperature)... Not a big difference, but it does confuse me a bit.

please note that the coefficients in practically all the panel specifications I ever saw are not provided for the same opperation point:

the coefficient for current I is normally given for short circuit (indicated by SC)the coefficient for voltage V is normally given for open circuit (indicated by OC)the coefficient for power P is normally given for maximum power point (indicated by MPP)

These coefficients are not provided to perform a calculation of IV curves at non STC condidtions, but they are provided for the layout of inverters or battery controllers.Three factors are predominantly to be considered:

Max current permissive: This is the short circuit current ISC of the pv array. And this increases when reducing the temperature. Thus the ISC at the lowest temperture possible needs to be considered.

Min voltage required to run the controller / inverter. Since the voltage reduces with increasing temperature one has to choose the number of panels high enough to remain even at very high temperture above the lowest operation limit of the controller/ inverter. Otherwise the mpp tracking of the controller/ inverter will be compromised.

Max voltage that the controller/ inverter can take: One has to choose the number of panels low enough that at even the lowest tempertures possible the open circuit voltage (not the mpp voltage) will be below the max voltage of the controller/ inverter. Otherwise the capacities in the DC part of the controller/ inverter will blow.

Please note that the coefficients are given in % of the specified value. And teh coefficient of current is two magnitudes smaller than for voltage and power.

It is not clear how you could observe these changes.Is this based on ambient temp? How would you measure cell temp?It is likely that an array will not have uniform cell temps. The hotter they get the greater the cell temp... and Vmp mismatching possibly.With 3 strings... 1 string that responds more to high temps would pull dow power more than Vmp.Then there is a question of the MPPT tracking? If the tracking is catching up to the real Vmp when it is getting warmer Vmp will stay higher then. I saw this on an Astronergy data sheet.Pmp coef. = -.469%/CVmp coef. = -.463%/CHave you checked this with a single module?

You misunderstand, I think. This is not based on observation, this is coming from the spec sheet. The coefficients you quote are very close - but for my panels, and for many others I've seen, including e.g. samsung, these values are much further apart - around a tenth of a percent per C. The thing is, I don't understand how that can be the case unless the temperature coefficient of Impp is also meaningfully negative, which I don't believe it should be. How can power decrease faster than voltage with temperature, unless current is also decreasing with temperature?

I see now. I think there is a discrepancy with many of the specs out there. Using a database of nearly 20,000 crystalline modules I averaged the Voc and Pmp and this is what I came up with.Ave. Pmp temp coef = -.44 %/C; Ave. Voc temp. coef = -.337 %/CThat is an ave ratio of Pmp/Voc temp coef's = 1.3Pmp should be reasonably close to Vmp so if there are specs that are much different that this ratio I would guess that the specs are not correct.